Question

maths solve all quiz​

Answer 1

Option (1) –6 is correct.

$\bullet \: \: \: \bf{ \Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \times \Bigg( \dfrac{8}{3} \div \dfrac{4}{9} \Bigg) = - 6}$

Given :

• An equation, $\bf{ \Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \times \Bigg( \dfrac{8}{3} \div \dfrac{4}{9} \Bigg)}$

To Find :

• The value of the given equation, $\bf{ \Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \times \Bigg( \dfrac{8}{3} \div \dfrac{4}{9} \Bigg)}$

Solution :

We have to find the value of the given equation, $\bf{ \Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \times \Bigg( \dfrac{8}{3} \div \dfrac{4}{9} \Bigg)}$

Method I :-

Solve it direct.

$\bf \implies\Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \times \Bigg(\dfrac{8}{3} \div \dfrac{4}{9} \Bigg) \\ \\ \\ \bf \implies\Bigg( \dfrac{ - 2- 5}{7} \Bigg) \times \Bigg(\dfrac{ \bigg( \dfrac{8}{3} \bigg) }{ \bigg( \dfrac{4}{9} \bigg)} \Bigg) \\ \\ \\ \bf \implies\Bigg( \dfrac{ - 7}{7} \Bigg) \times \Bigg( \dfrac{8}{3} \times \dfrac{9}{4} \Bigg) \\ \\ \\ \bf \implies\Bigg( - 1\Bigg) \times \Bigg(\dfrac{ \not72}{ \not12} \Bigg) \\ \\ \\ \bf \implies( - 1) \times (6) \\ \\ \\ \bf \implies - 6$

Hence,

The value of the given equation, $\bf{ \Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \times \Bigg( \dfrac{8}{3} \div \dfrac{4}{9} \Bigg)}$ is $\bf -6$

The option (1) –6 is correct.

Method II :-

Let us divide the given one equation into two equations and solve them, then multiply the result of the both equations.

$\bullet \: \: \: \bf\Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \: \: .........(1) \\ \\ \\ \bullet \: \: \: \bf \Bigg( \dfrac{8}{3} \div \dfrac{4}{9} \Bigg) \: \: ..........(2)$

First, we need to solve the equation (1),

$\bf \implies\Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \\ \\ \\ \bf \implies\Bigg( \frac{ - 2 - 5}{7} \Bigg) \\ \\ \\ \bf \implies \Bigg( \dfrac{ - 7}{7} \Bigg) \\ \\ \\ \bf \implies( - 1)$

Hence, the value of the 1st equation is –1.

Now, solve the equation (2),

$\bf \implies\Bigg( \dfrac{8}{3} \div \dfrac{4}{9} \Bigg) \\ \\ \\ \bf \implies\Bigg( \dfrac{ \bigg(\dfrac{8}{3}\bigg)}{\bigg(\dfrac{4}{9} \bigg)} \Bigg) \\ \\ \\ \bf \implies\Bigg( \dfrac{ \not8}{ \not3} \times \dfrac{ \not9}{ \not4} \Bigg) \\ \\ \\ \bf \implies(2 \times 3) \\ \\ \\ \bf \implies(6)$

Hence, the value of the 2nd equation is 6.

Now, multiple the results of the both equations,

$\bf \implies( - 1) \times (6) \\ \\ \\ \bf \implies - 1 \times 6 \\ \\ \\ \bf \implies - 6$

Hence,

The value of the given equation, $\bf{ \Bigg( \dfrac{ - 2}{7} - \dfrac{5}{7} \Bigg) \times \Bigg( \dfrac{8}{3} \div \dfrac{4}{9} \Bigg)}$ is $\bf -6$

The correct option is (1) –6.